The BAe 146/ RJ 85 RJ 100 use electric start (LF 507 engines). It;s not done via the IDGs (as only two of the engines are fitted with IDGs).
It's actually quite handy compared with air starting because when the APU is u/s, it's a lot easier to get a ground power cart than a huffer.
Also huffers tend to vary a great deal in efficacy.
There might be a weight penalty but really the whole a/c is a bit of a weight penalty!